To help facilitate the development of a theoretically rigorous and practically useful theory of customer value propositions (CVP), as called for repeatedly by the extant literature, this paper establishes a game-theoretic theorem regarding the dynamics of market competition and potential market entry. On top of this result and by employing logical rigor and analytical reasoning, eight generally true facts are developed without suffering from the constraints of data-and anecdote-based approaches, as widely used in the literature. In particular, these established results reveal how a newly adopted CVP is associated with the three essential processes underlying a company's operation, how it will be pivotal for the company to attain competitive advantages, how the value added by adopted CVPs can be determined, etc. At the end, recommendations for decision-making managers and entrepreneurs and potential questions for future research are provided.